ORDINARY LEVEL
PHYSICS
PRACTICAL WORK BOOK
BY
The Department of physics @ CRANE HIGH SCHOOL, 2020.
NAME: .........................................................................................................................................................
CLASS: .................................................................................... STREAM: ...............................................
0
TABLE OF CONTENTS
INTRODUCTION ............................................................................................................... 2
RECORDING OF PRACTICAL RESULTS ............................................................................ 3
WORKED OUT EXAMPLES ............................................................................................. 14
MARKING GUIDE .......................................................................................................... 23
CHAPTER ONE: MECHANICS EXPERIMENTS.................................................................. 24
CHAPTER TWO: LIGHT EXPERIMENTS............................................................................40
CHAPTER THREE: ELECTRICITY EXPERIMENTS ........................................................... 58
1
1.0 INTRODUCTION TO PHYSICS PRACTICAL
1.2 The students therefore should:
• Read through the experiment, reflect on its objective and
title
• Identify the quantities to be actually measured and those to
be calculated or derived as well as the given quantities
which control the experiments
• Draw a detailed columnar table of results for all the
measurements that are to be repeated and their associate
calculations.
Note
All values given to control the extent of performing the
experiment should be filled in the first column of the table while
keeping the order in which they are stated and the units
1.1:
INTRODUCTION 535/3 PHYSICS
Physics is sometimes called the science of measurements
because without observation and measurement it would not
exist.
• In order to develop and test theories it is important to make
measurements that are precise and accurate
• This workbook therefore discusses the recording of
measurements and data manipulation at ordinary level
(UCE).
1.2 Ordinary Level Physics Practical course should enable
students to:
• Carry out experiments on fundamental laws and principles
encountered in the theoretical work e.g. Hooke’s law,
Snell’s law, Principle of moments etc.
• Carry out measurements in the determination of a wide
variety of physical constants e.g. acceleration due to
gravity, refractive index of glass or liquid, mass of a Metre
rule, density of a substance, internal resistance of a cell,
focal length of a lens or mirror, resistance per Metre of a
wire.
• Gain experience of a variety of measuring instruments and
learn to handle them with skills and also appreciate their
limitations.
Column headings (Table of results)
• A closed columnar table of results with only three
horizontal lines should be drawn.
• Al columnar headings must be labeled and should consist
of a quantity and a unit or without a unit as the case may
be.
• The unit is separated from the quantity by enclosing it in
brackets. e. g a length l measured in centimeters may be
represented as follows – l (cm) but not length l (cm).
• Avoid the use of equations in column headings especially
when the quantity has been defined, e. g when the extension
is calculated from e= (P1-P0), the column heading should be
e (cm) but not e= (P1-P0) (cm).
• However, (P1-P0) (cm) is a good column heading when the
extension e is not defined.
• Avoid column headings such as l1-l2 (cm) or
(cm) rather
1.3 Objectives of the practical exam are to test students on;
• The ability to handle apparatus and use measuring
instruments effectively and safely
• The ability to plan the presentation of practical work
• The ability to interpret, evaluate and report upon
observations and experimental data
use (l1-l2) (cm) and
1.4 To students, each student should possess the following
scholastic materials;
• Long transparent rule, Scientific calculator, Geometrical
set, Sharp pencil and a rubber, Graph paper
•
When a quantity has not been assigned a symbol, choose an
appropriate symbol or letter to represent it. e. g.
Suppose a step in the procedure reads:  Determine the time for 20 0scillations.
 Choose a letter, say, t, to represent the time for 20
oscillations, instead of writing time for 20 oscillations as a
column heading.
 The first letter of the names of the quantity is usually
preferred. t- for time, m- for mass, l-for length, h-for height,
p-for pointer positions.
The duration of the Practical paper is 2 hours and 15 minutes.
(15 minutes for reading and planning, 2 hours for working).
Question one – always mechanics question and compulsory
Question Two – always light or heat
Question Three – always-current electricity
1.1 Columns of calculated quantities.
Some quantities can be calculated from a formula or given
expression and you should not omit steps that lead to the
final results of the formula e. g when asked to tabulate your
results including values of:
 Cos2 , you must progress from to cos and then cos2 you
must therefore have a column for
and then cos2 ..
Options
Total number of questions to answer is 2, each question is 30
marks, and whole paper is marked out of 60 marks.
PLANNING THE EXPERIMENT (15 MINUTES)
1.1 The purpose is to help students to:
• Think ahead and plan, Set up the apparatus as shown in the
diagram, Avoid making careless mistakes due to panic
• Properly record data with appropriate units
For
2
, progress from x to 𝑥2 then
.
 Units of calculated quantities can be derived from the formulae or
equations that relate different quantities
e.g. Column labeled can have the VA -1 OR Ω as its units.
RECORDING PRACTICAL RESULTS
All the raw reading of a particular quantity should be recorded
to the same number of decimal places and should be consistent
with the precision and accuracy of the apparatus
1.2 Units of calculated quantities.
The values recorded during the Physics Experiment Practical,
are divided into three. i.e.
Each reading recorded from an instrument should consist of two
parts namely: a) A numerical value recorded to the nearest smallest scale
division.
b) Units.
(a) Given values of varying quantity: These are usually given
in the procedures. They must be recorded the way they are
given in the instructions unless told to record otherwise.
(b) Experimental values (or measured values): These are
values of a varying quantity that are determined using an
instrument. They are recorded to the accuracy of the
instrument used. For example;
N.B
When given an instrument for carrying out measurements one
need to study the scale and establish the least Count or What 1
small scale division represents and then Units.
Table A:
Instrument
Recording measurements in an experiment
(i) Single measurement (The procedure does not require
repeating)
 Examples of single measurement:
• Width of metre rule;
• Width of a glass block;
• Rough distance of the image of a distant object in a concave
mirror or convex lens.
Metre-rule
Foot ruler
Stop clock
Quantity
measured
& Length
Time
Unit
Accuracy
(Number of
decimal places)
(cm)
1 dp.
(s)
Stop watch
Time
(s)
Ammeter
Current
(A)
Voltmeter
Voltage
(V)
Protractors
Angles
(0)
Measuring
cylinders,
Burettes,
Pipettes
Thermometer
Volume
(cm3)
or
(ml)
Temperature
1 dp.
(last digit
.0 or .5)
8.0s,
10.0s,
22.5s, 55.0s
2 dp
1.20s, 4.07s,
50.00s, 54.38s.
2 dp/1dp
0.14A, 0.22A,
0.58A, 0.90A
2 dp/1dp
0.35V, 0.80V,
1.25V, 2.95V
 Take the required measurement at least three times and then
calculate the average of the measured values and give its
value to the degree of accuracy of the measuring
instrument.
• The measured results may be put in table and the average
calculated outside the table.
• If the measurement is required to be recorded in SI units,
then record all the values in S.I units before finding the
average.
 In some cases a single measurement is taken once. For
example, in experiments using a helical spring the initial
position of the pointer before attaching a mass on it is
recorded once.
0dp. e.g.19°
50° 87°,32°
7ml, 15ml,
49ml.
(ii) Repeated measurement (Certain steps of the procedure
are required to be repeated for given values)
 These measurements are put in the main table of results to
the accuracy of the instrument used.
 In any column the number of decimal places in that column
must be the same.
0
C
1dp with .0 or
.5
Row data consist of readings or measurements taken directly
from a measuring instrument.
The main table of results should have only values of varying
quantities
Constant values of non-repeated quantity should be recorded
before the main table of results.
It should be expressed to a fixed number of decimal places
dictated by the scale of the instrument the units used and the
precision of the instrument.
3
Rule #4: Leading zeros. Zeros to the left of the first non-Zero
digit are NOT significant. Example; 0.000034 has only 2 s.f,
0.001111 has 4 s.f, 0.0075m, 0.000089m, 0.00037m are
expressed to 2 s.f
(c) Derided quantity values
 The values of trigonometric ratios and logarithms are
recorded to 3dp
Rules for determining the number of decimal
places in a column:
 Calculated values:
These are usually obtained from the experimental values.
The number of decimal places or significant figures to which
these values are to be recorded is obtained using the two basic
rules of data manipulation. These are;
(i) Decimal Places
The number of decimal places (dp) is the number of digits to
the right end of a decimal point. E.g. the number 3.6420 is
given to 4dp.Thus 3.6420 ≈ 3.642(3dp), 3.6420 ≈ 3.64(2dp),
3.6420 ≈ 3.6(1dp), 3 .6420 ≈ 4 (0dp).
1. Addition and subtraction of quantities.
 The number of decimal places (dp) in the answer should be
the same as the least number of dps in any of the numbers
being added or subtracted. E.g.
 (i) 4.721 (3dp) + 1.18 (2dp) = 𝟓.𝟗𝟎 (𝟐𝐝𝐩)
(ii) Significant Figures
The Significant Figures of a number refer to those digits that
have meaning in reference to a measured or specified value.
Correctly, accounting for Significant Figures is important while
performing arithmetic so that the resulting answers accurately
represent numbers that have computational significance or
value.
(ii) 420.03(2dp) + 299.270(3dp) + 99.068(3dp)
= 818.368 = 𝟖𝟏𝟖.𝟑𝟕(𝟐𝐝𝐩).
 420.03 is the least precise (2 decimal places). So the answer
818.368 MUST BE rounded to 2 decimal places to give
818.37 (2Decimal place)
There are four rules that are used to determine how many
significant figures are in a number. There are also rules for
determining how many digits should be included in numbers
computed using addition/subtraction, multiplication/ division,
or a combination of these operations.
(iii) 504.009(3dp) + 246.8(1dp) − 119.32(2dp)
=𝟔𝟑𝟏.𝟔(𝟏𝐝𝐩). .
Rules for determining how many Significant Figures are in
a number:
Rule #1: Non zero digits (1 – 9). Every counting number in a
recorded measurement is significant
Examples: - 5.39 has three significant figures, 1.892 has four
significant figures, 1.37mm, 5.42cm, 99.8 cm are expressed to
3 s.f.
Rule #2: Trapped zeros. Zero between counting numbers are
significant. Example; 4023 has four significant figures, 50014
has five significant figures, 10.5cm, 9.06cm, 2.04, 504 have 3
s.f
Rule #3: Trailing zeros.
 Zero at end of a number and with counting numbers to their
left is significant. Example: 1.00m, 0.300m, 2.50m, 10.0cm
are expressed to 3 sf.
 Trailing zeros are not significant numbers in case the
number has no decimal point. They just sense as place value
holders to show the magnitude of a number. Example:
470000 has 2 s.f, 400 has 1 sf, 300, 500, 80000, 1000000
are expressed to 1sf.
 Zeros as a result of measurement instrument are
significant. Eg 200, 20.0cm, 15.0s, 30g etc
Note. 39.9 rounded to 2sf is 40. [Please note the decimal point
at the end of the trailing zero. It makes the zero trapped and
hence significant]
4
2. Multiplication & division of quantities
The number of significant figures (s.f) in the answer should be
the same as the least number of s.f in any of the numbers being
multiplied or divided. E.g.
(i)
(v)
(53.4) 2 = 2852 (0dp) and not 2850 (3sf) as the rules
could have predicted, because the value 2850 (3sf) would
increase the error seriously.
(vi)
(2400) (3.45) (16.21) = 134218.8 = 134219
The number 2400 only has 2 Significant Figures (and it’s the
least no. of sfs), so the answer 134218.8 must be rounded to 2
Sf’s to give 130000. However, this creates a very large error, so
we just round off to a whole number 134219.
Thus if the number of significant figures before a decimal point
exceed those predicted by rule, then just round off to a whole
number (0dp).
(v) For reciprocals, squaring, Cubing, multiplying with a
float and dividing by a float, write the final answer to the
number of significant figures as the number being dealt
with.
Note: A float is a whole number or a constant, which has an
infinite number of decimal places e.g. 1, 20, 100, etc. A float
is not an experimental value. It’s only used in calculations and
does not affect the number of significant figures. E.g.
4.90 (3s.f). Not considering 1 because
it’s a float value.
Other examples, if x = 2.32,
X2 = (2.32)2 = 5.38, x3 = (2.32)3 = 12.5
5
MANIPULATION OF DATA IN THE TABLE
Finding the number of significant figures for calculated values in the main table of results
Largest value in the column (i.e Largest product, Largest quotient, or Largest reciprocal) is used to determine significant figures of
the rest of the processed values in that column. Largest value has the largest number of significant figures.
Example 1
𝒍=𝟎.𝟓𝟎𝟎𝒎
𝑥(c𝑚) 𝑥(𝑚)
𝑦(𝑐𝑚) 𝑦(𝑚)
𝑥
𝑦
𝑥𝑦(𝑚2)
1
xl(m2) 𝑥𝑙
(𝑚) (𝑚−1 )
𝑦
𝑦
5.0
0.05
26.1
0.261
0.01
0.003
0.19
0.03
0.11
10.0
0.10
31.0
0.310
0.03
0.010
0.32
0.04
0.13
15.0
0.15
38.0
0.380
0.06
0.023
0.39
0.08
0.21
20.0
0.20
45.0
0.450
0.09
0.040
0.44
0.10
0.20
25.0
0.25
53.2
0.532
0.13
0.063
0.47
0.13
0.24
30.0
0.30
62.0
0.620
0.19
0.090
0.48
0.15
0.24
 In the column of
𝒙𝒍
𝒚
, using the largest value in this column, we have;
log𝑥𝑦
. Thus, all values in this column
should be recorded to 2dp.
 In the column of 𝑥2, using the largest value in the columns of x, we have; 0.30(2𝑠𝑓) ×0.30(2𝑠𝑓) =𝟎.𝟎𝟗𝟎(2𝑠𝑓). Thus, all values in the
column of 𝑥2 should be recorded to 3dp.
Example 2
𝑬=𝟑.𝟎𝟎𝑽 (𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆)
𝑣
(Ω)
𝐼
𝐸
𝑉
1 −1
(𝑚 )
𝑦
𝑦(𝑚)
V(V)
I(A)
1 −1
(𝑣 )
𝑣
0.200
0.50
0.40
2.000
2.5
1.3
6.0
5.00
0.300
0.60
0.36
1.667
2.8
1.7
5.0
3.33
0.400
0.70
0.32
1.449
3.1
2.2
4.3
2.50
0.500
0.90
0.28
1.1 11
3.6
3.2
3.3
2.00
0.600
1.00
0.24
1.000
4.2
4.2
3.0
1.07
0.700
1.10
0.20
0.909
5.0
5.5
2.7
1.43
1
𝐼
 In the column of , the values are given precisely to 3 d.p. In the column of , the values of voltage were measured from a voltmeter
to the accuracy of 2dp. Similarly, In the column of , the values of current were measured from an ammeter to the accuracy of 2dp.
 In the column of
, using the largest value in the column V i.e 1.10, we have;
𝟏(𝒇𝒍𝒐𝒂𝒕)
𝟏.𝟏𝟎(𝟑𝒔𝒇)
=𝟎. 𝟗𝟎𝟗(𝟑𝒔𝒇). Thus, all values in this
column should be recorded to 3 dp. (for reciprocals, squares, multiplication or division by float, we use the largest value in
the previous column)
1
In the column of , using the largest value in the column of I i.e 0.40, we have;
𝐼
 . Thus, all values in this column should be recorded to 1 dp.
6
𝟏(𝒇𝒍𝒐𝒂𝒕)
=𝟐. 𝟓(𝟐𝒔𝒇)
𝟎.𝟒(𝟐𝒔𝒇)
 In the column of
, using the largest quotient value in this column, we have;
. Thus, all values in this column
should be recorded to 1 dp.
 In the column of
we have;
, using the largest value in this column y i.e 0.700 , Hence,
𝟏(𝒇𝒍𝒐𝒂𝒕)
𝟎.𝟕𝟎𝟎(𝟑𝒔𝒇)
=𝟏. 𝟒𝟑(𝟑𝒔𝒇) . Thus, all values in this column should be recorded to 2 dp.
Example 3.
𝑙(𝑚)
𝑙3(𝑚3)
𝑡(𝑠)
T(𝑠)
𝟎.𝟗𝟎𝟎(𝟑𝒔𝒇)
𝟎.𝟕𝟐𝟗(𝟑𝒔𝒇)
𝟏𝟕.𝟕𝟓(𝟒𝒔𝒇)
𝟎.𝟖𝟖𝟕𝟓(𝟒𝒔𝒇)
These values
were given
precisely to
3d.p
0.400
(3 dp)
0.0640
These values
were
obtained
from a stop
watch to 2d.p
6.50
𝟎.𝟕𝟖𝟕𝟕(𝟒𝒔𝒇)
(4 dp)
0.3250
(4 dp)
0.1056
 In the Column of 𝒍𝟑; Using the largest value in the column of , we have; 0.900(3𝑠𝑓) ×0.900(3𝑠𝑓) ×0.900(3𝑠𝑓) =0.729(3𝑠𝑓). Thus all
values in the column of 𝒍𝟑 should be recorded to 3dp.
 In the Column of
of
; Using the largest value in the column of , we have;
. Thus, all values in the column
should be recorded to 4dp.
 In the Column of 𝑻𝟐; Using the largest value in the column of T , we have; 0.8875(4𝑠𝑓) ×0.8875(4𝑠𝑓) =0.7877(4𝑠𝑓). Thus, all values
in the column of 𝑻𝟐 should be recorded to 4dp.
Example 4.
u(cm)
v(cm)
(u+v) (cm)
uv(cm2)
𝑣
𝑢
20.0
66.6
1332
3.33
25.0
41.7
1043
1.67
30.0
32.8
984
1.09
35.0
28.5
998
0.81
40.0
26.5
1060
0.66
45.0
24.2
1089
0.54
cos𝑢
log𝑣
log𝑢𝑣
 /For uv : Using the largest product, Largest value in this column, we have: 20.0(3𝑠𝑓) ×66.6(3𝑠𝑓) =𝟏𝟑𝟑𝟐(𝟎𝒅𝒑) . Thus, all values in
the column of uv should be recorded to 0dp.
 For : Using the largest quotient, in this column, we have:
. Thus, all values in the column of
recorded to 2dp.
7
should be
𝑖(0)
𝑟(0)
𝑥(𝑐𝑚)
𝑙(𝑐𝑚)
𝑠𝑖𝑛𝑖
𝑐𝑜𝑠𝑟
𝑥𝑐𝑜𝑠𝑟(𝑐𝑚)
10
6
0.8
7.0
0.156
0.996
0.8
20
14
1.6
7.2
0.342
0.970
1.6
30
20
2.4
7.4
0.500
0.940
2.3
40
28
3.5
7.8
0.643
0.883
3.1
50
30
4.0
8.1
0.766
0.866
3.5
60
35
4.8
8.5
0.866
0.819
3.9
sin2i
1
𝑠𝑖𝑛2 𝑖
For 𝒙𝒄𝒐𝒔𝒓: Using the largest product in this column of 𝒙𝒄𝒐𝒔𝒓, We have:
.𝟖𝟏𝟗(𝟑𝒔𝒇) ×𝟒.𝟖(𝟐𝒔𝒇) = . (𝟐𝒔𝒇). Hence values in column of 𝒙𝒄𝒐𝒔𝒓 (𝒄𝒎) to 𝟏 𝒅𝒑.
•
In the column for d, using the largest value, we've; d = x2–
x1
d = 13.0(ldp)-24.9(ldp)= - 11.9(ldp)..
All the values in the column of d (cm) should therefore be
written to 1dpl.
Example 5
Given that the-values of f0 (cm), xl(cm) and x2(cm)are
experimental values, all measured using a meter rule.
Complete the table of results for values of l (cm), d
(cm), d2(cm2) and (l2-d2) (cm2); where d = (X2- Xl)
and f0= 10.0cm.
•
d
In the column for d2, using the largest value we've;
(3Sf's) ,
SOLUTION
l(cm) l(cm)
xl (cm)
x2(cm) d(cm) l2 (cm2) d2 (cm2)
(l2-d2) (cm2)
6.5f0
65
52.0
8.8
-43.2
4225
1866
2359
6.0f0
60
46.6
9.2
-37.4
3600
1399
2201
5.5f0
55
36.2
11.0
-25.2
3025
635
2390
5.0f0
50
41.1
10.0
-31.1
2500
967
1533
4.5f0
45
30.0
11.9
-18.1
2025
328
1697
4.0f0
40
24.9
13.0
-11.9
1600
142
1458
It is important to note that the value 1866.24 is supposed to be
written to 3sf's (if we follow the rule for multiplication).
However, if the value 1866.24 is written to 3sf's we get 1870.
In this case, the error created due to rounding off is quite big.
Thus to minimize the rounding off error, we round this number
off but write it as a whole number i.e. round it off to remove the
decimal.
Thus, we write 1866.24 ≈ 1866(0dpl). Since the leading value
is to 0dpl, all the values in the column should be to 0dpl.
To determine the number of decimal places for the values in a
given column we first determine the number of decimal places
for the leading value in the column (i.e. by using the rules for
data manipulation) and then we write the remaining values to
the same number of decimal places.
In the column for l2, using the largest value we've;
l2=65.0(3s. f) x 65.0(3s. f) = 4225 (3s.f)
Thus, all values in the column should be written to 0dpl.
•
In the column for (l2-d2), using the largest value we have;
(l2-d2) = 4225(0dpl) - 1866(0dpl) = 2359(0dpl).
Thus, all values in the column should be written to 0dpl
Note:
 The above rules only apply to the largest value in a column
or columns under consideration.
 For uniformity, all values in a particular column in the
table must be written to the same number of decimal places
as the largest value in that column.
How the numbers of decimal places for the calculated values
in the above table of results were determined.
• Values of x1, and x2 are experimental values obtained using
a meter rule. They must be recorded to the accuracy of the
meter rule (i.e. 1dpl).
•
•
In the column for l, using the largest value we've;
6.5f0 = 6.5(2s.f) x 10.0(3s.f) = 65(2s.f).
Since the largest value is to 2sf and 0dps, all the values in
the column of l (cm) should be written to 0dp.
 In case the number of significant figures before a decimal
point exceeds those predicted by the rules, then just round
of to the nearest whole number.
 If the rules give constant values in a column, then increase
the number of significant figures by one.
8
Complete the tables below using the rules of data
manipulation above.
Table 1
Table 2
𝟏 −𝟏
(𝑽 )
𝑽
𝟏 −𝟏
(𝑨 )
𝑰
10.0
0.32
20.0
0.30
30.0
0.28
40.0
0.26
50.0
0.22
60.0
0.20
30.0
0.90
40.0
0.95
50.0
1.15
60.0
1.35
70.0
1.55
Table 3:
x(cm)
x2(cm2)
l(cm)
85.0
48.6
75.0
42.1
70.0
33.5
65.0
29.7
60.0
18.4
55.0
15.8
l2(cm2)
9
(x2-l2) (cm2)
𝟏 −𝟏
(𝑨 )
𝑰
Table 4:
l(m)
t(s)
time t for 10 oscillations
T(s)
T2(s2)
l3(m3)
0.9
17.75
0.8
Table 6:
d2(cm2)
y1(cm)
y2(cm)
41.0
15.3
24.6
15.25
46.0
13.5
31.8
0.7
12.95
51.0
12.5
37.5
0.6
10.60
56.0
11.8
42.7
0.5
8.40
61.0
11.5
48.1
0.4
6.50
66.0
11.0
53.4
Table 5: time t, for 20 oscillations
d(cm) 2θ(0) θ(0) 20T(s)
T(s)
70
120
24.5
2
2
T (s )
d(cm)
cos𝜃
a)
b)
c)
d)
Include values ofd2- (y2- y1)2.
Plot a graph of d 2- (y2- y1)2 against d.
Find the slope, S of your graph.
Calculate the focal length of the convex lens from; S= 4f.
60
95
26.0
50
76
27.5
Table 6:
40
60
28.5
R(Ω)
l(cm)
30
46
29.5
1
75.0
2
60.9
3
50.9
4
44.1
5
38.4
6
34.4
a)
Plot a graph of
a) Plot a graph of T2 against cos𝜃
b) Find the slope S of your graph.
Table 4:
t(cm)
x(cm)
y(cm)
1.5
1.7
2.6
1.7
2.1
3.2
1.9
2.3
3.6
2.1
2.5
3.8
2.3
2.8
4.2
2.5
3.0
4.6
x2(cm2)
y2(cm2)
(y2- y1)2(cm2)
(y2- y1)(cm)
(100−𝑙)
100−𝑙
𝑙
against R
b) Determine the slope S of the graph
c) Find the unknown resistance Rs from the
expression
a)
Plot a graph ofy2 against x2
b)
Find the slope s of your graph.
c)
Compute the critical angle C, of the glass
from expression;
10
GRAPH WORK
 For convenience use digits 1, 2, 2.5 and 5 then
submultiples e.g. 0.1, 0.2, 0.25 and 0.5; 0.01, 0.02, 0.025,
and 0.05 etc. and the multiples e.g. 10, 20, 25 and 50, 100,
200, 250 and 500, etc.
a. The Title of the graph at the top of the graph paper.
 Clearly written in only 1 line e.g. A graph of T 2 Against x2
(i.e. T2 plotted along the vertical axis & x2 along the
horizontal axis).
 No units should be included in the title.
 Must be noted as given in the procedures or instruction
requiring you to plot the graph.
Note: 4 & 8 are however not convenient digits though they are
at times used.
 If the value of
does not fall exactly on one of the
(ii) Axes
 Must be drawn perpendicularly to each other with an arrow
at the end of each axis.
 Each axis must be clearly and correctly labeled with the
quantity and unit in brackets.
 It must be clearly marked every after 10 small squares
(2cm) starting from the origin.
 The starting point of each axis must be clearly shown.
convenient scales, take the nearest upper value from the set
of convenient scales (i.e. the scale should be rounded to the
nearest greater (upper) suitable value of one significant
figure.
 In case the first nonzero digit is 1, make it 2. If it is 2, 3 or
4, make it 5. If it is 5, 6, 7, 8, or 9, make it 10.
1;
(iii) Intercepts
 The intercept on a particular axis is the value for the
quantity plotted along that axis for which, the quantity
plotted along the other axis is zero.
 Therefore, if the intercept on the vertical (y – axis) is
required, the starting point on the vertical can be anywhere
(i.e. any value slightly below the smallest value in the
column to be plotted on that axis) but the horizontal axis (xaxis) must start from zero. Similarly, if the intercept on the
horizontal axis is required, then the vertical axis must begin
from zero.
2
1.011
2
2.021
5
5.57
(iv) Scale
Obtaining the Suitable Convenient Scale
A scale is suitable if it covers at least 50% of the graph paper.
It is convenient if it is easy to plot and follow. It is consistent
along an axis, if it is uniform (has equal intervals) along that
axis.
0.00995432
Where;
HORIZONTAL
𝑅𝑎𝑛𝑔𝑒 𝑜𝑛 𝐻.𝐴
80
(This gives what one smallest square
represents on each axis of the
graph)
10
0.11344;
0.2
0.015432
0.02
0.31344
0.5
0.04;5432
0.05
0.6789
1
0.07432
0.1
0.01
VERTICAL
𝑅𝑎𝑛𝑔𝑒 𝑜𝑛 𝐻. 𝐴
𝑁𝑂. 𝑂𝐹 𝑆𝑄𝑈𝐴𝑅𝐸𝑆
1∶
5, 6, 7, 8, 9;
 Multiply by 10 to get what 2cm (10small squares)
represent.
 If the interval between zero and the 1st reading is extremely
bigger than the interval between the first reading and
second reading, then the first reading or lowest value
should be shifted closely to the origin or to the starting point
of that axis.
Obtain the range on both vertical axis (VA) and horizontal axis
(HA).
PROCEDURES
10
2, 3, 4;
5
1∶
Choosing the starting value along each axis
𝑅𝑎𝑛𝑔𝑒 𝑜𝑛 𝑉.𝐴
𝑁𝑂.𝑂𝐹 𝑆𝑄𝑈𝐴𝑅𝐸𝑆
𝑅𝑎𝑛𝑔𝑒 𝑜𝑛 𝑉.𝐴
•
100
•
•
11
When marking the axes, if the question does not involve
finding the intercept, the starting value should not
necessarily be zero. Start from a convenient value which is
smaller than and a bit distant from the smallest value in
the column.
The starting value on any axis should be a multiple of the
scale on that axis.
There are only two cases where the starting value on a given
axis must be zero, 0. These are:
(i)
When the smallest value (top or bottom value) in
a column is very close to zero.
(ii)
When an intercept is required on the other
(Perpendicular) axis.
 In order to plot a point accurately on a particular axis, get the
value to be plotted from the main table of results (without
rounding off), subtract the nearest value on that axis
from the value to be plotted, and then divide the result
by the scale of that axis. This gives the number of smallest
squares to be counted from the chosen nearest value when
plotting that value.
e. Line of best fit or best curve
Either the plotted points lead to a curve or best straight lines.
In the case of a straight line, then it should be a line through
most of the points leaving almost equal number of points on
either side if the points are scattered. This line should be
produced long enough to cut the axis.
Before using the Stopwatch, reset it such that it’s initial reading
is zero as in the figure above.
Examples
Convert the time t, in the figures below to seconds
f. Slope
When finding the slope, a large triangle covering all the plotted
points is drawn. The points to be used to find the slope should
be correctly read and written on the graph.
Slope =
ΔVertical
ΔHorizontal
(i)
(ii)
(iii)
(iv)
The reading is 34.56 seconds
The reading is 59.23 seconds
The reading is 6.40 seconds
The reading is 77.38 seconds i.e
1 × 60 + 17.38 = 77.38
(ii) Stop Clock
A reading on a stop clock is to one decimal place. i.e ; .0 or .5
The slope should have the appropriate units obtained from the
quantities of the labeled axes, except when it is a ratio of
quantities of the same unit.
 Calculation
Before substituting any quantity in the formula or expression, it
must be converted to S.I units first. The values should be
correctly substituted in the given expression.
 The accuracy of the final answer should be that of the least
accurate measurement involved in the calculation.
(i.e. put into account the rules of data manipulation).
Put the units of the quantity under investigation if any.
MEASUREMENT OF TIME
The instruments commonly used for measuring time in the
laboratory are the stop clock and stop watch. Before using these
instruments, ensure that the initial reading is zero.
In the figure, the reading of the stop clock is 60.5s or 0.5s
(to 1 decimal place).
In the 2 nd figure above, the stop clock reading for the pointer
in position A, B, C, D and E is as follows;
In position A, stop clock reading = 50.5s
In position B, stop clock reading = 52.0s
Stop clock
 It measures time in seconds. 1 small division on the scale
of stop clock=1s OR 1 small division = 0.5s
12
In position C, stop clock reading = 53.0s not 52.8s, In position D, stop clock reading = 54.0s not 54.4s, In position E,
stop clock reading =55.0s
If the smallest division on the stop clock is 0.5s, like the one above, then values of time are recorded to 1dp. However,
if time are recorded to1the Smallest division is s,of 0dpa(s whole numbers)It is important to note that values recorded
to a wrong number in the lie of decimal places are marked wrong even if they range for the correct values.


It is possible to estimate time to 1 d.p with both Stop Clocks.
Both Clocks record time to 1 d.p and the last digits in any values should be a 0 or 5. Typical Values are 8.0s, 10.0s, 22.5s, 55.0s
(i) Stop watch
The stop watch measures time in seconds(s) to two decimal places. All values of time obtained using a stop watch must be recorded to
two decimal places e.g. 7.23, 25.56, 48.89 etc.


The Stop Watch records time to the nearest 0.01s (2 d.p)
Every reading recorded with this Stop watch must therefore be recorded to 2 d.p. Typical readings 1.20s,
4.07s, 50.00s, 54.38s. Wrong readings 7.321s, 20s, 41.6s, 48.0s
Note : The stop watch may give values of time in minutes, seconds and microseconds. These values should be converted and
recorded in seconds. Values of time should be recorded in minutes only when they are required in minutes.
13
WORKED EXAMPLES
Example 1:
In this Experiment, you will investigate the relationship between the depression of a loaded beam and the distance
between the supports.
Procedure.
a) Attach a pointer at the 50cm mark of the meter rule, use cello tape.
b) Place the meter rule so that it lies horizontally on the two knife edges provided.
c) Clamp a scale vertically and place it near the 50cm mark of the meter rule as shown in the figure below.
d) Adjust the knife-edges such that the distance x between them is equal to 90cm and they are equidistant from 50cm
mark of the metre rule.
e) Read and record the position of the pointer on the scale.
f) Suspend a mass, m of 500g at the 50cm mark of the metre rule
g) Read and record the position of the pointer on scale. Hence find the depression, D, of the metre rule at its midpoint
h) Remove the mass from the metre rule.
i) Repeat the procedures (d) to (h) for values of x=80cm, 70cm, 60cm, 50cm, and 40cm.
j) Enter your results in a suitable table including values of log10Dand log10𝑋
k) Plot a graph of log10D (along the vertical axis) against log10D (along the horizontal axis)
l) Find the slop, N, of the graph.
SOLUTION
Recording single readings:
e) Let Po be the initial position and pointer and P be the new position of the pointer
Po= 80.0cm.Then D = P - Po g) P = 84.8cm; D = P - Po
= 84.8cm - 80.0cm
= 4.8cm
Recording repeated readings:
j) The table of results
X(cm)
90
80
70
60
50
40
P(cm)
84.8
82.8
81.7
81.2
80.6
80.3
D(cm)
4.8
2.8
1.7
1.2
0.6
0.3
log10 X
log10 D
1.954
1.903
1.845
1.778
1.699
1.602
0.681
0.447
0.230
0.079
- 0.222
- 0.523
i) From the graph,
Slope; N =
1.24
N = 0.395
𝐍 = 𝟑. 𝟏𝟒
NOTE: Calculation for the scale should be done as side work and should not be included on the answer
sheet because no marks are awarded for the working.
SIDE WORK
x
Horizontal scale (log10 - axis)
Vertical scale (log10D –axis)
1:
𝑅𝐻𝐴
1:
1:
1:
1:
80
𝑅𝑉𝐴
100
.
0.352
1:
80
1: 0.044
1: 005
1: 0.01204
1: 0.02
1 small square = 0.005
10 small squares = 0.05
1 small square = 0.02
10 small squares = 0.2
15
Example 2
In this experiment, you will be required to determine the acceleration due to gravity using a pendulum bob.
Apparatus
Thread (130cm long), pendulum bob, retort stand with clamp and a stop clock
Procedure
(a) Suspend the pendulum bob from a retort stand such that it is at a distance h = 0.10 m from the floor.
(b) Adjust the length of the pendulum to 1.20 m.
Table Top
θ
Thread
Pendulum bob
Fig. 2
Floor
h = 0.10
(c) Displace the bob through a small angle θ as shown in Fig. 2 above. Release it to oscillate in a vertical plane.
(d) Determine the time for 20 oscillations.
(e) Find the time, T, for one oscillation.
(f) Raise the pendulum bob (by reducing the length of the pendulum) by a distance
and 0.60 m and in each case repeat procedures (c) to (e).
(g) Record your results in a suitable table including values of T2.
(h) Plot a graph of T2 against h.
(i) Find the slope, s, of the graph.
(j) Calculate the acceleration due to gravity, g, from the expression
16
h = 0.20, 0.30, 0.40, 0.50
SOLUTION
Recording single readings:
Let t be the time for twenty oscillation
a) For h = 0.10,
d) t = 20T = 44.5s;
Recording repeated readings:
e) The table of results
h(m)
0.10
0.20
0.30
0.40
0.50
0.60
t(s)
44.5
43.0
41.0
39.0
36.5
34.5
T2(s2)
4.97
4.62
4.20
3.80
3.35
2.99
T(s)
2.23
2.15
2.05
1.95
1.83
1.73
i) From the graph,
g) Slope S from A to B;
h) From;
𝑆=−3.8 𝑠2𝑚−1
NOTE: Calculation for the scale should be done as side work and should not be included on the answer sheet
because no marks are awarded for the working.
SIDE WORK
Vertical scale (T2 –axis)
Horizontal scale (h-axis)
1:
1:
𝑅𝐻𝐴
80
0.6−0
1:
80
1:
1:0.0075
1:0.01
𝑅𝑉𝐴
100
4.
1:0.0198
1:0.02
1 small square = 0.01 m
10 small squares = 0.1 m
1 small square = 0.02 s2
10 small squares = 0.2 s2
17
Example 3:
In this experiment, you will determine the refraction index ‘n’ of a glass block provided.
Procedure
a) using the drawing pins provided, fix the plain white sheet of paper on a soft board
b) place the glass block in the middle of the sheet and using a pencil, mark the outline PQRS of the glass block
c) Remove the glass block. Draw perpendicular to PQ at point1B,
.5 cm from P
A
P1
P2
i
P
B
Q
y
S
x
R
C
P3
P4
d) Draw a line AB such that angle
i = 100
e) Replace the glass block on white sheet of paper on its outline.
f) Stick two pins P1and P2along AB and looking through the glass block the opposite face SR, stick other pins P3 and
P4 in line with the images of P1 and P2. Remove the glass block
g) Join C and D. Measure and record the distance x and y
h) Repeat procedures (d) to (h) for values for i = 20, 30, 40, 50, 60, and 70 0
i)
Enter your results in a suitable table including values of
j)
Plot a graph of
k) Find the slope, n, of your graph
Apparatus
Glass block, white sheet of paper,4 optical pins, 4 drawing pins, soft board and a complete geometry set
18
SOLUTION
Recording single readings:
h) For i =100 ,x = 1.0 cm, y = 6.6 cm
Recording repeated readings:
j) The table of results
i(0) x(cm)
y(cm)
10
20
30
40
50
60
6.6
6.7
7.0
7.4
7.6
8.0
1.0
1.5
2.4
3.2
3.8
4.6
𝑥
𝑦
sin𝑖
0.15
0.22
0.34
0.43
0.50
0.58
0.174
0.342
0.500
0.643
0.766
0.866
l) From the graph,
NOTE: Calculation for the scale should be done as side work and should not be included on the answer sheet
because no marks are awarded for the working.
SIDE WORK
Vertical scale ( sini –axis)
Horizontal scale ( - axis)
1:
1:
𝑅𝐻𝐴
1:
80
1:
0.
𝑅𝑉𝐴
100
0.
1: 0.00692
1: 0.01
1 small square = 0.01
10 small squares = 0.1
1: 0.005375
1: 0.01
1 small square = 0.01
10 small squares = 0.1
19
20
CODE
D1
D2
D3
D4
D5
R1
R2
SAMPLE MARKING GUIDE FOR THE ABOVE QUESTION
DESCRIPTION
Tracing the outline PQRS of the glass block
Drawing a perpendicular at point B1 =1.5cm from P
Drawing a line AB such that angle I =10o and sticking pins P1 and P2 along AB
Sticking pins P3 and P4 in line with the images of P1 and P2
Drawing a line through pin marks P3 and P4 to meet SR at C and joining C and B
Sub-total
o
Recording the values of x to 1dp when I =10 and unit: range
(0.8 – 4.8) (cm) value = ½
;unit: (cm) = ½ mrk
Recording the values of y to 1dp when i = 10o and unit range
mrk; unit (cm) = ½ mrk
MARKS
= ½mrk
= ½mrk
= ½mrk
= ½mrk
= ½mrks
2½marks
=1mrks
(6.4 – 8.6) (cm) value = ½ =1mrks
T1
Design of the table of results with 5 columns, i– column labeled with unit i(o) and all values =½mrk
entered
T2
Label of the rest of the values of x increasing to 1dp (1.3 – 1.7),
T3
G1
G2
G3
G4
G5
G6
C1
C2
C3
C4
(2.2-2.6), (3.0-3.4), (3.6-
=2½mrks
4.0) and ( 4.4 - 4.8) (cm)
(@½ mrk)
Recording 6 values of sini and x/y correctly calculated (any 3 correct) (@½ mrk)
Sub-total
Title of the graph; A graph of sini against x/y
The label of the axes with units; sini and x/y
(@½ mrk)
Suitable and convenient scales for the axes covering at least 50% of graph paper (@½ mrk)
=3mrks
08 marks
=½mrk
=1mrk
=1mrk
6 correctly plotted points
(@½ mrk)
The best straight line to fit the plotted points
The method of finding the slope. Big triangle covering all plotted points
Sub-total
Calculation of the slope, n
Correct substitution
Arithmetic
Accuracy
Sub-total
TOTAL
=3 mrks
=½ mrk
=½ mrk
6½ marks
=1½mrk
=½ mrk
=½ mrk
=½ mrk
03marks
20 marks
TOPIC1: MECHANICS EXPERIMENTS
1.01 Experiment 01
In this experiment, you will determine the mass, m of a metre rule.
(a) Balance the metre rule provided on a knife-edge with the graduated side facing upwards.
(b) Note the balance point P and record its distance, lo, from end B.
(c) Place a mass m of 10 g on top of the metre rule at the 10 cm mark and balance the arrangement as shown
in Fig. 1 below.
m
Metre
Fig. 1
lo
P
A
l1
10 cm
Knife edge
rule B
l2
(d) Read and record the distances l1 and l2.
(e) Repeat the procedures (c) and (d) for values of m = 20, 30, 40, 50 and 60 g.
(f) Record your results in a suitable table including the values of (l2 – lo) and
(g) Plot a graph of m against
.
.
(h) Find the slope, m of your graph.
Apparatus: Knife edge; Metre rule; One mass of 10 g, Two masses of 20 g, One mass of 50 g
22
1.02 Experiment 02
In this Experiment, you will investigate the relationship between the depression of a loaded beam and the distance
between the supports.
Procedure.
a) Attach a pointer at the 50cm mark of the meter rule, use cello tape.
b) Place the meter rule so that it lies horizontally on the two knife edges provided.
c) Clamp a scale vertically and place it near the 50cm mark of the meter rule as shown in the figure below.
d) Adjust the knife-edges such that the distance x between them is equal to 90cm and they are equidistant from 50cm
mark of the metre rule.
e) Read and record the position of the pointer on the scale.
f) Suspend a mass, m of 500g at the 50cm mark of the metre rule
g) Read and record the position of the pointer on scale. Hence find the depression, D, of the metre rule at its
midpoint
h) Remove the mass from the metre rule.
i) Repeat the procedures (d) to (h) for values of x=80cm, 70cm, 60cm, 50cm, and 40cm.
j) Enter your results in a suitable table including values of log10D and log10𝑋
k) Plot a graph of log10D (along the vertical axis) against log10D (along the horizontal axis)
l) Find the slop, N, of the graph
Apparatus, a retort stand with clamp, a pointer, two knife edges, a metre rule and half metre rule; 500g mass.
23
1.03 Experiment 03
In this experiment, you will determine the mass Mc of a loaded meter rule
(a)
Balance a loaded meter rule on the knife edge as shown in figure 1
(b)
Read and record the balance length, lo, from end A of the meter rule.
(a)
Suspend a mass m = 50g at a distance, x = 5.0cm from end A
(b)
Balance the system on a knife edge as shown in figure 2 above
(c)
Read and record the new balance length, y.
(d)
Repeat procedures (a) to (c) for values of x = 10.0, 15.0, 20.0, 25.0 and 30.0 cm
(e)
Enter your results in a suitable table including values of (y - x) and (lo – y
(f)
Plot a graph of (y –x) against (lo – y).
(g)
Find the slope, S, of the graph
(h)
Calculate, Mc, from the expression: Mc = 50xS
Apparatus: loaded meter rule, 50g mass, knife edge and wooden piece of wood
24
1.04 Experiment 04
In this experiment, you will determine the weight of a meter rule;
PART I
(a)
Read and record the mass mo labeled on the meter rule in kilograms
(b)
Calculate the weight wo = 10mo
PART II
(c)
Balance the meter rule on a knife edge
(d)
Read and record the balance point xo, on the meter rule
(e)
Suspend a mass m = 0.100kg at the 10.0cm mark
(f)
Balance the meter rule on the knife edge
(g)
Read and record the new balance point x1
(h)
determine the values of L1 = (x1 – 10.0) and L2 = (x0 –x1)
(i)
Repeat procedures ( E) to (h) for values of m = 0.150, 0.200, 0.250 and 0.300kg
(j)
Tabulate your results including values of L =L1 – L2
(k)
Plot a graph of L against m
(l)
From the graph, read the values of m when L = 50.0cm
(m)
Determine the weight w1 = 10m
(n)
Determine the value w =
𝑤0 +𝑤1
2
Apparatus: a meter rule, a spring balance, 50g masses and 100g masses
25
1.05 Experiment 05
In this experiment you will determine the density, ⍴, of the rubber bug provided.
(a) Record the mass, M of the meter rule provided.
d1
d2
d
Fig. 5
W
Wooden block
(b) Suspend the rubber bung, W, at a distance d = 5 cm from the zero end of the metre rule.
(c) Balance the metre rule with its graduated face upwards on the knife edge as shown in Fig.3 above.
(d) Measure and record the distances, d1 and d2, of the knife edge from the zero and 100 cm marks of the
metre rule respectively.
(e) Repeat procedures, (b) to (d) for values of d equal to 10, 15, 20, 25 and 30 cm.
(f) Tabulate your results, including values of (d2 – d1) and (d1 – d).
(g) Plot a graph of (d2 – d1) against (d1 – d).
(h) Find the slope, S, of your graph.
(i) Determine the density, ⍴, of rubber from the expression;
⍴ = 0.5 S.
Apparatus: Rubber bung; a meter rule labelled with its mass M; knife edge; wooden block, 20 cm × 15 cm
×15 cm and a piece of thread, 20 cm.
26
1.06 Experiment 06
In this experiment you will determine the density of water.
(a) Record the radius, r, of the small beaker (or can) provided
Small beaker
Scale
Bottle top
Sand
h
Fig. 6
Water
Large beaker
(b) Place the small beaker (or can) into the large beaker containing water.
(c) Add small quantities of sand gradually into the small beaker until the beaker floats upright in the water
as shown in Fig. 4 above. Make sure the small beaker does not touch the sides of the large beaker.
(d) Place three bottle tops into the small beaker.
(e) Read and record the depth, h, by which the small beaker sinks.
(f) Repeat procedures (d) and (e) for 6, 9, 12 and 15 bottle tops.
(g) Record your results in a suitable table.
(h) Plot a graph of number of bottle tops against h.
(i) Find the slope, S, of the graph.
(j) Calculate the density of water, ⍴, from the expression
2.5 S = ⍴πr2.
Apparatus A small beaker with its radius r indicated and linear scale using a graph paper strip attached;
a large beaker; 15 soda bottle tops; small amount of sand and water.
27
1.07 Experiment 07
In this experiment, you will determine the relative density of a liquid, Ɩ provided.
Fig.7
Procedure
a) Clamp the spring provided vertically and suspend the empty beaker as show in Fig.5
b) Record the initial position of the pointer on the metre rule.
c) Pour volume, V= 50 cm3 of water into a beaker and record the new position of the pointer. d) Find the
extension, x produced.
e) Repeat the procedures (c) to (d) for V= 100, 150, 200 and 250 cm3.
f) Pour out water and dry the beaker.
g) Repeat the procedures (a) to (e) using the liquid Ɩ and find its extension, y produced.
h) h) Record results in a suitable table.
i) Plot a graph of y against x
j) Determine the slope, S of the graph.
Apparatus: Liquid, Ɩ (paraffin or Cooking oil or Petrol), water, Retort stand with 2 clamps, Metre rule,
pointer, spiral spring, thread, measuring cylinder and a beaker.
28
1.08 Experiment 08
In this experiment, you will determine the acceleration due to gravity, g using a spiral spring.
Apparatus:
A retort stand with 2 clamp, 5 masses of 50 grams on a hanger, 1 spring, stop watch or clock, metre rule, pointer.
Fig. 8
PART ONE
a)
b)
c)
d)
e)
f)
g)
h)
Suspend the spiral spring provided from a clamp as shown in Fig. 6.
Read and record the position of the pointer on the metre rule.
Suspend the mass, M = 50 g from the free end of the spiral spring.
Read and record the new position of the pointer, find the extension, e of the spring.
Repeat the procedure in (c) and (d) for values of M = 100, 150, 200, and 250 g.
Tabulate your results in a suitable table.
Plot a graph of e against M.
Find the slope, S1 of the graph.
PART TWO
a) Remove the metre rule.
b) Displace the mass, M =50 g suspended from the spring through a small vertical distance and release it.
c) Determine the time, t for 20 oscillations.
d) Find the periodic time, T for an oscillation
e) Repeat the procedures (b) to (d) for values of M =100, 150, 200, and 250 g.
f) Enter your results in a suitable table including values of T and T2.
g) Plot a graph of T2 against M
h) Determine the slope, S2 of the graph.
i) Find the value of acceleration due to gravity, .From;
29
1.09 Experiment 09
In this experiment, you will determine the acceleration due to gravity.
(a) Suspend the pendulum bob from a retort stand as shown in Fig. 10 below.
Thread
Bench Top
θ
l
Fig. 9
Pendulum bob
(b) Adjust the length of the pendulum, l, so that it is equal to 0.90m.
(c) Displace the bob through a small angle θ as shown in Fig. 7 above. Release it to oscillate in a vertical
plane.
(d) Determine the time, t, for 20 oscillations.
(e) Find the time, T, for one oscillation.
(f) Repeat procedures (b) to (e) for values of l = 0.80, 0.70, 0.60, 0.50 and 0.40 m.
(g) Record your results in a suitable table including values of T 2.
(h) Plot a graph of T2 against l.
(i) Find the slope, s, of the graph.
(j) Calculate the acceleration due to gravity, g, from the expression;
.
Apparatus A pendulum bob, a string about 120 cm, a stop clock, metre rule and retort stand with a clamp.
30
1.10 Experiment 10
In this experiment you are required to determine the acceleration due to gravity, g.
(a) Clamp the spring provided with a pointer attached and a metre rule as shown in Fig. 8 below.
Clamp
Spring
Pointer
Retort stand
Meter rule
Fig. 10
(b) Read and record the initial position Po of the pointer on the meter rule.
(c) Attach a mass, m, equal to 0.100 kg on the spring and record the new position P1 of the pointer. Hence,
find the extension, x, in meters.
(d) Pull the mass downwards through a small distance and release it.
(e) Measure and record the time for 20 oscillations.
(f) Calculate the time, T, for one oscillation.
(g) Repeat the procedures (d) to (f) for values of m equal to 0.200, 0.300, 0.400 and 0.500 kg
(h) (h) Record your results in a suitable table including values of T 2.
(i) Plot a graph of T 2 against m.
(j) Find the slope, s of the graph.
(k) Calculate g from the expression; g =
𝟒𝟎𝝅𝟐 𝒙
𝒔
Apparatus A spring with a pointer, five 100 g masses on a mass hanger, stop clock, and a metre rule
(or half metre rule); and retort stand with a clamp.
31
1.11 Experiment 11
In this experiment, you will determine the relative density, ⍴ of the material of solid X provided.
Meter rule
A
z
d
Fig. 11
Q
P
y
Water
X
B
100 g
Beaker
(a) Record the mass, M, of the solid X provided.
(b) Suspend a metre rule from a clamp using a piece of thread and adjust it until it balances horizontally.
(c) Read and record the distance of the balance point, P, of the rule from end A.
(d) Suspend the solid, X at a distance d = 10 cm from end A of the metre rule and immerse it completely in
water in the beaker.
(e) Suspend a 100 g mass from a point, Q, between P and B and then adjust the position of Q until the meter
rule balances horizontally, with X completely immersed and not touching the beaker as shown in Fig. 9
above.
(f) Measure and record distances z and y.
(g) Repeat procedure (d) to (i) for values of d = 15, 20, 25, 30 and 35 cm.
(h) Enter your results in a suitable table.
(i) Plot a graph of z against y.
(j) Find the slope, s, of the graph.
(k) Calculate the relative density, ⍴, of the material from the expression;
𝑀
⍴ = 𝑀−100𝑆
Apparatus: Plastic Beaker, Metre rule, 100 g mass, 3 pieces of thread of 30 cm each, solid x, with its mass M
indicated, water.
32
1.12 Experiment 12
In this experiment, you will determine Young’s modulus for wood.
Desk-Top
80 cm
G – Clamp
Fig. 12
M
Rubber band
Metre ruler
(a) Record the thickness, d, of the metre rule.
(b) Clamp the metre rule provided with the graduated face upwards such that the free length equals 80 cm as shown
in Fig. 10 above.
(c) Attach a mass, M equal to 0.05 kg at the end of the metre rule using a rubber band or thread.
(d) Depress the mass through a small vertical distance and release it to oscillate.
(e) Measure and record the time for 20 oscillations. Find the period, T.
(f) Repeat the procedures (c) to (e) for M equal to 0.10, 0.15, 0.20, 0.25 and 0.30 kg
(g) Record your results in a suitable table including values of T2.
(h) Plot a graph of T2 (along the vertical axis) against M (along the horizontal axis).
(i) Find the slope, S, of the graph.
(j) Calculate Young’s modulus, Y, for wood from;
Apparatus: G-Clamp; Wooden metre rule with its thickness, d indicated; one 50 g mass; Three
100 g masses; Rubber band; Stop clock
33
1.13 Experiment 13
In this experiment, you will determine the spring constant of the spiral spring
provided.
(a) Clamp the spring using the two pieces of wood provided and make sure that the spring is vertical as
shown in Fig. 11(a) below.
(b) Attach a pointer to the free end of the spring. Read and record the pointer position xo on a vertical metre
rule.
Fig.13 (a)
Fig.13 (b)
(c) Suspend a mass, m = 0.100 kg from the lower end of the spring as shown in Fig.14 (b) above.
(d) Read and record the new position of the pointer x1.
(e) Repeat procedures (c) and (d) above for the values of m = 0.200, 0.300, 0.400, 0.500 and 0.600 kg.
(f) Record your results in a suitable table including values of the extension, e in metres.
(g) Plot a graph of e against m.
(h) Find the slope, S, of the graph.
1
(i) Determine the elastic constant, k from k = 𝑆
Apparatus, A spring with a pointer; Six 100 g masses on a mass hanger; and a metre
rule; and retort stand with a clamp.
A spring with a pointer; Six 100 g masses on a mass hanger; and a metre rule; and retort stand with a
34
TOPIC 2: LIGHT EXPERIMENTS
Glass blocks: Glass blocks of any dimensions can be used. However, that of 100mm × 60mm × 18mm is
preferred.
Glass Prisms: Equilateral triangular prisms should be used unless stated otherwise.
Mirrors and Lenses: The suitable focal length of a mirror or lens should be smaller than the smallest value of the
object distance.
Eg in experiment 22, the smallest object distance d=15cm, the suitable mirror is that of f=10, or 5 cm. In experiment
32, the smallest object distance u = 30 cm, the suitable lens is that of f= 25, 20, 15, 10 or 5 cm.
•
•
•
A PROTRACTOR
A Protractor measures angles in degrees (°)
A small division on a protractor is an angle of 1° (0 d.p)
Since 1° has no decimal place angles measured with a
protractor should be recorded without a decimal place e.g.
19°,50°,87°𝑎𝑛𝑑 32°.
A protractor measures angles between two intersecting lines in degrees
(°) to zero decimal places. All values of angles
obtained using a protractor must be recorded to zero decimal
places (as whole numbers) e.g. 10°, 9°, 23°, 64° etc.
Protractors usually have two sets of numbers going in opposite
directions. Be careful which one you use! When in doubt think
"should this angle be bigger or smaller than 90° "
RULERS (eg. Metre – Rule)
The different types of rulers are 15cm ruler, 30 cm rulers, halfmetre rule and a metre-rule. They are all used in the same way.
 The metre rule measures lengths in Centimetres (cm)
 1 Small division on the scale is equal to a length of 0.1cm
 This Value has one decimal place and it means that all
measurements with a metre rule should be recorded to 1 decimal
place in cm
 In metres 0.1cm = 0.001m, so when measurements on a
metre rule are converted into metres, they should be
recorded to 3 decimal places following the fact that ;
1Small division= 0.1cm = 0.001m(3d.p)
How to Measure an Angle with a Protractor?
Step 1
The zero line of the protractor needs to be lined up with one side
of the angle.
Step 2.
You read the set of numbers from your zero line to the line where
the angle stops.
Step 1. To draw an angle of 50 degrees first draw a line segment
⇒ 𝟏𝟎𝐝𝐢𝐯𝐢𝐬𝐢𝐨𝐧𝐬 = 𝟏𝐜𝐦
that is to be the one side of the angle.
1 cm
Step 2
1 division =
= 0.1 cm
10
Then put the protractor so that its zero line matches with your
line segment and that the vertex is in place. From; 0 to 1, 1 to 2,
2 to 3, etc, there are 10 equal divisions.
.
Step 3. Now put a mark at the 50-degree point.
Step 4. Then take the protractor off and draw a line through your mark.
.
.
35
FOR RULER ABOVE,
Therefore, any reading from rulers is accurate 1 decimal place. Hence, such readings should be recorded to 1dp.
Length AB=1.0cm+6×0.1cm
Length AB=1.6cm
Or Length AB=16×0.1=1.6cm
2.01: Experiment 14:
In this experiment, you will investigate the relationship between the number of images n formed by two plane
mirrors inclined to each other and the angle between the mirrors.
(a) Draw two lines such that they make an angle θ = 900 at the point of intersection as shown in the figure 12
below.
Plane mirror B
Optical pin
Plane mirror A
Fig. 14
(b) Place mirrors A and B as shown above on the lines drawn
(c) Place an optical pin at a distance of about 6cm in front of the point of intersection of the two mirrors such
that it is equidistant from the two mirrors.
(d) Count and record the number of images, n observed. (place the eye at a distance of more than half a metre
away from the mirrors)
(e) Keeping mirror A on the line, repeat procedures (c) and (d) adjusting the position of B such that it makes
the angle θ =700, 600, 400and 300.
(f) Enter your results in a suitable table including values of
(g) Plot a graph of n against
(h) Find the intercept, C, on the n-axis (i) Find the slope of the graph.
Note: Hand in your working sheet.
Apparatus: 2 mounted plane mirrors, 4 drawing pins, 1 optical pin, and Complete Mathematical set.
36
2.02 Experiment 15
In this experiment, you will be required to verify that the angle of incidence is equal to the angle of reflection.
(a) Fix a white sheet of paper, provided on the soft board and place the plane mirror vertically on it.
(b) Put the plane mirror on the white sheet of paper and trace the mirror line with a sharp pointed pencil as shown
in Fig.13 below.
Fig. 15
(c) Remove the mirror from the paper. Label the traced line as AB.
(d) Draw a normal MN bisecting the mirror line AB (e) Draw a line PN at angle i = 10o to MN.
(f) Fix pins P1 and P2 along the line PN.
(g) Place the mirror back on the paper so that it’s reflecting surface coincides exactly with the mirror lining AB you
have drawn.
(h) View the images of P1 and P2 in the mirror.
(i) Fix pins P3 and P4 such that they are in line with images of P1 and P2.
(j) Remove the pins P1, P2, P3 and P4 and the mirror from the white sheet of paper.
(k) Draw a line NS passing through the marks of pins P3 and P4.
(l) Measure and record the angle r, between MN and NS.
(m) Repeat procedures (e) to (l) for angles i = 20o, 30o, 40o, 50o, 60o and 70o.
(n) Record your values of i and r in a suitable table.
(o) Draw a graph of i against r and find its slope.
37
2.03 Experiment 16
In this experiment, you will verify that the angle of incidence, reflected ray and the normal line at the point of
incidence, all lie in the same plane.
Procedures
a) Fix the plain sheet of paper on the soft board provided
b) Draw a line RS in the middle of the white sheet of paper provided.
c) Draw a normal ANM on RS as shown in Fig. 14.
𝐀
y
Plane mirror
𝐍
𝐑
𝐂
x
𝐒
𝐏𝟏
Fig. 16
d)
e)
f)
g)
h)
i)
j)
l)
m)
𝐏𝟐
𝐌
𝐁
Measure the distance NM, x = 1.5cm and fix a pin at M
Place the mirror along the mirror line RS as shown in Fig. 14 above
View the image of the pin at M from the right hand side of the normal ANM and fix pin P1, and P2 such that
they are in the line with the image of the pin at M
Remove the pins P1 and P2 and the mirror from the white sheet of paper
Draw a line BCA passing through the marks of pin P1 and P2 to meet the normal at A.
Measure and record the distance y between the points N and A
Repeat procedures (d) to (i) for x = 2.0cm, 3.0cm, 4.0cm, 5.0cm 6.0cm 7.0cm and 8.0cm k) Record your
results in suitable table
Plot a graph of x (along the vertical axis) against y (along the horizontal axis)
Find the slope S of your graph.
N.B: Staple your working sheet inside the work book.
Apparatus: A place mirror, soft board, white sheet of paper, 3 optical pins, 4 drawing pins and
complete geometry set.
38
2.04 Experiment 17:
In this experiment, you will determine focal length, fof a concave mirror.
Fig. 17
Procedure
a) Set up the apparatus as shown in fig. 15 above.
b) Adjust the distance, 𝒅 = 𝟏𝟓 𝐜𝐦 and close the switch.
c) Adjust the position of the screen to and fro until a sharp image of the filament of the bulb is seen on the
screen.
d) Open switch.
e) Measure and record the distance, V from the mirror to the screen.
f) Repeat the procedures (b) to (e) for values of, 𝒅 = 𝟐𝟎, 𝟐𝟓, 𝟑𝟎, 𝟑𝟓 and𝟒𝟎 𝐜𝐦.
g) Enter your results in a suitable table including values of
h) Plot a graph of
against V.
i) Find the slope, S of the graph.
j) Calculate the focal length, f from the expression;
Apparatus:
2 cells, Torch bulb (lamp), Concave mirror, White screen, Switch, Mirror holder, Metre rule, paper
39
2.06 Experiment 18
In this experiment, you will determine the focal length of a concave mirror.
(a) Align the torch bulb, the concave mirror and the screen as shown in Fig. 16 below.
Concave
mirror
White
screen
Torch
bulb
Mirror
holder
K
Dry cells
Fig. 18
d
v
(b) Adjust the distance, d to 15 cm.
(c) Close switch K.
(d) Adjust the position of the screen to obtain a sharp image of the filament of the bulb on the screen.
(e) Open the switch K.
(f) Measure the distance, v, of the screen from the mirror.
(g) Repeat the procedures (b) to (f) for values of d = 20, 25, 30 35 and 40 cm.
(h) Record your results in a suitable table including values of
𝑉
(i) Plot a graph of 𝑑 against v.
(j) Find the slope, S, of the graph.
(k) Calculate the focal length, f, from the expression ; f =
𝟏
𝑺
Apparatus: Switch, 2 dry cells, torch bulb on its holder, connecting wires, mirror or lens holder, concave mirror
focal length = 10 cm and a white screen.
40
2.07 Experiment 19
In this experiment, you will determine the focal length, f, of concave mirror provided.
(a) Fix the mirror in the holder.
Concave mirror
Illuminated object
u
White screen
Switch
Mirror
holder
Fig. 19
v
(b) Focus light from a window onto the screen.
(c) Measure and record the distance, x, between the screen and the mirror.
(d) Arrange the mirror, the mounted bulb and the screen as shown in Fig. 17 above.
(e) Adjust the object distance u = 2.4x
(f) Close the switch and move the screen until a sharp image of the object is formed on it.
(g) Measure and record the image distance, v.
(h) Repeat the procedures (e) to (g) for values of u = 3.2x, 4.0x, 4.8x, 5.6x and 6.4x.
(i) Enter your values in a suitable table including values of (u + v) and uv.
(j) Plot a graph of uv against (u + v).
(k) Find the slope, f, of the graph.
(l) Calculate the difference between f and x.
Apparatus: Switch, 2 dry cells, torch bulb on its holder, connecting wires, mirror or lens holder,
concave mirror focal length = 10 cm and a white screen.
41
2.08 Experiment 20
In this experiment, you will determine the refractive index of, n, of a glass block.
(a)
Using the drawing pins provided, fix the white sheet of paper on a soft board.
(b)
Place the glass in the middle of the sheet of paper and using pencil, mark the outline PQRS, of the glass
block.
A
P1
P2 i
P
Q
B
y
C
S
x
R
P3
Fig. 20
P4
D
(c)
Remove the glass block and draw a perpendicular to PQ at B.
(d)
Draw a line AB such that angle, 𝑖 = 10o and replace the glass block.
(e)
Stick two pins P1 and P2 along AB.
(f)
Looking through the glass block from the opposite face SR, stick two other pins P3 and P4 in line with
the images of pins P1 and P2.
(g)
Remove the glass block and draw a line through P3 and P4 to meet SR at C.
(h)
Join C to B, measure and record distances x and y.
(i)
Repeat procedures (f) to (g) for values of i equal to 20o, 30o, 40o, 50o and 70o.
(j)
Enter your results in a table, including values of 𝑠𝑖𝑛 𝑖 𝑎𝑛𝑑
𝑋
𝑦
.
𝑋
(k)
Plot a graph of 𝑠𝑖𝑛 𝑖 against 𝑦
(l)
Find the slope, n, of the graph.
NOTE: Hand in the tracing Paper
Apparatus: Glass block; Soft board; 2 Thumb pins; 4 Optical pins; Plain sheet of paper
42
2.09 Experiment 21
In this experiment, you will determine the refractive index, n, of the material of
the glass block provided.
(a) Fix the plane sheet of paper on a soft board using drawing pins.
P1
ί
A
D
R
Q
P2
O
B
P
C
P3
Fig. 21
P4
S
(b) Place the glass block on the sheet of paper so that it rests on its broader face and trace its outline
ABCD.
(c) Remove the glass block.
(d) Measure angle i equal to 20o and draw line QO.
(e) Fix pins P1 and P2 on line QO and then replace the glass block onto its outline.
(f) Looking through the opposite face of the block fix pins P3 and P4 along RS such that they appear to be
in line with the images of pins P1and P2.
(g) Remove the pins and the glass block and draw a line through P3 and P4 to meet the glass block at R.
(h) Join R to O and measure angle θ.
(i) Repeat procedures (d) to (h) for values of i = 30o, 40o, 50o and 60o.
(j) Record your results in a suitable table including values of sin i and cos θ.
(k) Plot a graph of sin i against cos θ.
(l) Find the slope, n, of the graph.
HAND IN THE WHITE TRACING PAPER
Apparatus: Glass block; Soft board; 2 Thumb pins; 4 Optical pins; Plain sheet of paper.
43
2.10 Experiment 22
In this experiment, you will determine the refractive index, n, of the material of glass block given.
R
P1
P2
A
B
O
D
r
C
P
P3
Fig. 22
P4
Q
(a) Fix the plane sheet of paper on a soft board using drawing pins.
(b) Place the glass block on the sheet of paper so that it rests on its broader face and trace its outline ABCD.
(c) Remove the glass block.
(d) At point O about 2 cm from A, draw a line RO at an angle θ = 80o to AB.
(e) Fix pins P1 and P2 along RO and then replace the glass block onto its outline.
(f) Looking through side DC, fix pins P3 and P4 such that they appear to be in a straight line with the images of P1
and P2 as shown in Fig. 20 above.
(g) Remove the pins and the glass block and draw a line through P3 and P4 to meet DC at P.
(h) Join P to O.
(i) Measure angle r.
(j) Repeat procedures (d) to(i) for θ = 70, 60, 50, 40 and 30o.
(k) Record your results in a suitable table including values of cos θ and cos r.
(l) Plot a graph of cos θ against cos r.
(m) Find the slope, n, of the graph.
HAND IN THE TRACING PAPER
Apparatus: Glass block; Soft board; 2 Thumb pins; 4 Optical pins; Plain sheet of paper.
44
2.11 Experiment 23.
In this experiment you will determine the refractive index, , of a glass block.
R
M
P1
P2 𝛂
A
D
B
N
𝜃
C
S
P3
Fig. 23
P4
T
Procedures
a) Fix the plain sheet of paper on the soft board using drawing pins.
b) Place the glass block provided in the middle of the paper. Make sure that the glass block rests on its broad
face as shown in figure 21.
c) Trace the outline ABCD of the glass block.
d) Remove the glass block.
e) Mark a point N on AB such that AN is a quarter of AB.
f) Draw a line MN perpendicular to AB.
g) Draw a line RN at an angle 𝜶 = 𝟏𝟎𝒐 to MN.
h) Fix two pins P1 and P2 on line RN.
i) Place the glass block on its outline.
j) Looking through the glass block from side CD, fix two pins, P3 and P4 so that they appear to be in line with
the images of P1 and P2.
k) Remove the glass block and the pins and draw lines TS and SN.
l) Measure and record angle θ
m) Repeat procedures (g) to (l) for values of 𝜶 = 𝟐𝟎𝒐, 𝟑𝟎𝒐, 𝟒𝟎𝒐, 𝟓𝟎𝒐and𝟔𝟎𝒐.
n) Record your results in a suitable table including values of sin α and cosθ.
o) Plot a graph of sin α against cosθ
p) Find the slope of the graph.
Note: Hand in you tracing paper
Apparatus: Plain sheet of paper, rectangular glass block, soft board, 2 optical pins, 4 drawing pins, complete
mathematical set.
45
2.12 Experiment 24
In this experiment, you are required to determine the refractive index n, of the glass using glass prism.
Procedure:
(a) Place the glass prism on a plain sheet of paper on a soft board and draw its outline. Label the ver
PQR as seen in fig. 22 below.
tices
𝐐
𝒊
𝐀
𝐏𝟐
𝐁
𝐫
𝐏𝟑
𝐏𝟒
𝐏𝟏
𝐏
Fig. 24
(b) At point A, 2cm from vertex Q, draw a normal to the line PQ.
𝐑
(c) Draw a line DA at an angle of incidence, i =300with the normal.
(d) Stick pins P1 and P2 about 4cm apart on the line DA.
(e) Replace the glass prism on its outline such that its vertices exactly match those on the outline.
(f) Stick pins, P3 and P4 such that they are collinear with the image of P1 and P2.
(g)
Remove the prism and the pins. Draw a line through the position of the pins P3 and P4 to meet RQ at B.
(h) Join B to A measure and record angle r.
(i) Repeat procedure (c) to (h) for values of i = 400,500,600and 700.
(j) Enter your results in a suitable table including values of sin i and sin r.
(k) Plot graph of sin (along the vertical axis) against sin (a long the horizontal).
(l) Find the slope, n, of your graph.
Note: Hand in your tracing paper
Apparatus: Plain sheet of paper, rectangular glass block, soft board, 2 optical pins, 4 drawing pins, complete
mathematical set.
46
2.13 Experiment 25.
In this experiment, you will determine the focal length, f, of the lens, L, provided.
(a) Arrange the cross wires, the lens, L and the screen in a straight line as shown in Fig. 23 below.
Cross wires Lens holder
White screen
Lens, L
Torch bulb
K
Fig. 25
Dry cells
u
v
(b) Adjust the distance, u between the cross wires and the lens to 30 cm.
(c) Close the switch, K so that the bulb lights.
(d) Move the screen to and fro until a sharp image of the cross wires is formed on the screen.
(e) Read and record the image distance, v, between the lens and the screen.
(f) Repeat procedures (b) to (e) for values of u equal to 40, 50, 60 and 70 cm.
(g) Record your results in a suitable table including values of
𝑉
𝑉
𝑈
(h) Plot a graph of 𝑈 against v.
(i) Find the intercept, f1, on the v – axis.
(j) Find the slope, S, of the graph.
1
(k) Calculate, f2, from, f2 = 𝑆
.
(l) Find f from the expression; f =
𝑓1 +𝑓2
2
Apparatus: Switch, 2 dry cells, torch bulb in its holder, connecting wires, cross wires, lens holder, convex lens
focal length = 10 cm and a white screen.
47
2.14 Experiment 26.
In this experiment, you will determine the focal length of a converging lens.
(a) Mount the lens provided and place it facing the window.
(b) Place the screen behind the lens and adjust it until a clear image of the distant object is obtained.
(c) Measure and record the distance, d, between the lens and the screen.
Wire
Gauze
Lens
White screen
x
Fig. 26
y
(d) Arrange the bulb, wire gauze, lens and screen as shown in Fig. 24 above.
(e) Adjust the lens so that the distance, x between the wire gauze and the lens is equal to 2.5d.
(f) Close the switch and move the screen until a clear image of the wire gauze is obtained on the screen.
(g) Measure and record the distance, y, between the wire gauze and the screen.
(h) Repeat procedures (e) to (g) for values of x = 3.0d, 3.5d, 4.0d and 4.5d.
(i) Record your results in a suitable table including values of (y – x) and x(y – x).
(j) Plot a graph of (y – x) against x(y – x).
(k) Determine the slope, S, of your graph.
1
(l) Calculate f from the relation: S = 𝑓
Apparatus: Switch, 2 dry cells, torch bulb on its holder, connecting wires, cross wires, lens holder, convex
lens of focal length = 10 cm and a white screen.
48
2.15 Experiment 27
In this experiment, you will determine the focal length, f, of the lens provided.
(a) Focus the image of a distant object onto the screen provided.
(b) Measure and record the length, fo, between the screen and the lens.
(c) Connect the bulb, the dry cells and switch, K, in series as shown in figure 34 below.
White screen
Lens
Wooden
K
x
y
Fig. 27
(d) Arrange the bulb, lens and the screen as shown in Fig. 25 above.
(e) Adjust distance, x, between the bulb and the lens to 1.5fo (f) Close the switch, K.
(g) Adjust the position of the screen to obtain a clear image on it.
(h) Measure the distance, y, between the lens and the screen.
(i) Repeat procedures (e) to (h) for x = 2.0F, 2.5F, 3.0F and 4.0F.
(j) Tabulate your results including values of xy and x + y.
(k) Plot a graph of xy against x + y.
(l) Find the slope, f, of the graph.
Apparatus: Switch, 2 dry cells, torch bulb in its holder,a wooden small piece of block, connecting wires, cross
wires, lens holder, convex lens of focal length = 15 cm or 20 cm and a white screen.
49
3.16: Experiment 28.
In this experiment, you will determine the focal length of the converging lens provided.
(a) Mount the lens in the holder provided and place it facing a window.
(b) Place a white screen behind the lens.
(c) Adjust the position of the white screen until a clear image of a distant object is obtained on it.
(d) Measure and record the distance, f, between the lens and the white screen.
(e) Connect the bulb, dry cells and the switch, K in series.
(f) Arrange the bulb, wire gauze, lens and the white screen as shown in figure 26 below.
Wire gauze
White screen
Lens
K
x
y
Fig. 28
(g) Adjust the lens so that the distance, x, between the wire gauze and the lens is equal to 2.0f.
(h) Close switch, K, and move the white screen until a clear image of the wire gauze is obtained on the white
screen.
(i) Measure and record the distance, y, between the lens and the white screen.
(j) Open switch, K.
(k) Repeat procedures (g) to (j) for values of x = 2.4f, 2.8f, 3.2f and 3.6f.
(l) Record your results in a suitable table including values of xy and (x + y).
(m) Plot a graph of xy against (x + y).
(n) Determine the slope, F, of the graph, where Fis the focal length of the lens.
(o) Find the value of:
𝐹−𝑓
𝑓
.
Apparatus: Switch, 2 dry cells, torch bulb on its holder, a wooden small piece of block, connecting wires,
lens holder, convex lens of focal length = 15 cm and a white screen.
50
3.17 Experiment 29
In this experiment, you will determine the power, P of a cylindrical water lens using two methods. Procedure
METHOD I
a) Measure and record the external diameter, D, of the 250ml glass beaker provided.
b) Draw using a pen, a vertical line along the strip of the paper provided.
c) Stick the strip of paper vertically on the side of the glass beaker using the pieces of cello tape provided.
d) Place the beaker containing water between the screen and the illuminated object such that the vertical line
on the beaker faces you as shown in the figure 27 (a) below.
White screen
Beaker
Water
Vertical line
K
x
y
Fig. 29 (a)
e) Pour water into the beaker up to the 250 ml mark.
f) Adjust the distance, x, to 20.0 cm.
g) Adjust the position of the screen until a sharp vertical line image of the bulb is formed on it.
h) Measure and record the distance, y, of the screen from the bulb.
i) Calculate the value of, P, from the expression;
j) Repeat the procedure (f) to (i) for x = 30.0 cm.
k) Calculate the average value of P.
DO NOT DISMANTLE THE SET UP
METHOD II
White screen
Beaker
K
b
Fig. 29(b)
u
𝜸
51
a) Adjust the distance between the bulb and the screen to ,𝜸 = 5Dcm as shown in the fig.37(b) above.
b) Starting with the beaker near the screen, move the beaker towards the bulb until a sharp diminished vertical
line image of the bulb is formed on the screen.
c) Measure and record the distance, u, of the beaker from the bulb.
d) Keeping , constant, move the beaker further towards the bulb until another sharp magnified image is
formed on the screen.
e) Measure and record the new distance, b, of the beaker from the bulb.
f)
Repeat procedure (a) to (e) for values of 𝜸 = 6D, 7D, 8D, 9 D and 10D cm.
. h) Plot a graph of 𝑧
g) Tabulate your results including values of
against 𝛾.
i) Find the slope, S of the graph.
j) Calculate the value of, P, from the expression;
Apparatus: 2 dry cells, 1 double cell holder, 1 torch bulb, a bulb holder, 1 switch, 1 250ml glass beaker,
water, 1 screen, connecting wires, 1 meter rule, wooden block, 1 piece of paper 2cm X 4cm and 2 pieces of
transparent cello tape, vernier calipers.
52
TOPIC 3: ELECTRICITY
EXPERIMENTS
Constantine wire SWG 28 and SWG 30: For experiments that have only the ammeter, SWG 30 is preferred
because it has a smaller resistance leading to bigger values of current, I that are easier to read.
Similarly, for experiments that have only the Voltmeter, SWG 28 is preferred because it has a higher resistance
leading to bigger values of potential difference, V that are easier to read.
Bulbs, 2.5V. A 2.5V bulb in a circuit will give light only if the P.d across it 2.5V or more. This therefore means
that a bulb in a circuit may light or may not. As long as the connected Ammeters and Voltmeters deflect, the
student should continue with the experiment regardless of whether the bulb lights or not.
In some experiments, the bulb may not give light at first but as the experiment progress, it gives light. This means
that initially, the pd across the bulb was far below 2.5V. In other experiments, the bulb may give light at first but
as the experiment progress, it goes off. This means that the P.d across the bulb has fallen below 2.5V.
The connections should be firm enough and the circuits should be connected from the positive of the battery to the
negative of the battery.
To make the connections easily, first place the instruments as they appear in the circuit diagram. The terminals must
correspond i.e,
 The positive (RED) knobs (terminals) of the ammeters or voltmeters must be connected to the positive side of
the cell(s) in the circuit.
 The negative (BLACK) knobs (terminals) of the ammeters or voltmeters must be connected to the negative side
of the cell(s) in the circuit.
In this way, the meters may be facing away from you, but after connecting, you can turn the meters to face you for
easy reading.
 If the terminals are interchanged, (i.e when Positive is connected to negative), the meters will deflect in the
opposite direction. The pointer will move to the left of the zero (0) mark. You may be tempted to think that the
meter is not working because it deflects by a small amount to the left of zero. When it deflects this way, the
student should inter change the terminal connections.
 All the connections should be firm. If not the meters may not deflect or if they do, the deflections will not be
steady! This makes taking the reading hard.
 After taking the reading the student should remember to switch off the circuit to avoid un necessary drop in the
e.m.f of the cell(s) during the experiment.
53
54
3.01: Experiment 30.
In this experiment, you will determine a constant of the wire provided.
(a) Connect the circuit shown in the figure 31 below starting with a length of the wire, y, equal to 30 cm.
Dry cells
Wire
Cello tape
K
y
V
Fig. 30
Cello tape
(b) Close switch K.
(c) Read and record the reading, V , of the voltmeter (d) Open switch K.
(e) Repeat procedures (c) to (e) for the values of y = 40, 50, 60 and 70 cm.
1
𝑉
(f) Record your values in a suitable table including values of and
1
1
(g) Plot a graph of 𝑉 against 𝑦
(h) Find the slope, s, of the graph.
1
𝑦
.
1
(i) Determine the intercept, c, on the 𝑉 axis.
(j) Calculate the constant of the wire,  , from the expression; 
=
100𝑐
𝑠
Apparatus: Voltmeter (0-3 V); 2 Dry cells; Jockey; Cello tape; 5 pieces of connecting wires; Metre rule;
Switch; Nichrome (28SWG).
55
3.02 Experiment 31
In this experiment, you will determine the resistivity, ρ, of the bare wire, W.
(a) Connect the ammeter A, switch K, dry cell E and wire W as shown in figure 42 below.
Bare wire
E
K
Cello tape
A
d
Fig.31
Cello tape
(b) Adjust distance, d, of the wire to 20 cm.
(c) Close the switch, K, and record the reading, I, of the ammeter.
(d) Repeat the procedures (b) and (c) for values of d equal to 30, 40, 50, 60, 70 and 80 cm.
(e) Record your results in a suitable table including values of
(f) Determine the slope, S, of the graph.
1
𝐼
against d.
(g) Calculate the resistivity, ρ, of the wire from; ρ = 1.6 x 10-5 S.
Apparatus: Ammeter (0 – 1 A); 1 Dry cell (Size D); Jockey; Cello tape; 5 pieces of connecting wires;
Metre rule; Switch; Constantan (28 SWG)
56
3.03: Experiment 32.
In this experiment, you will determine the resistivity, , of the material of the material of the wire
provided.
Bare wire
K
Cellotape
A
ι
Fig. 32
V
Jockey
Cellotape
(a) Connect the circuit as shown in figure 43 above.
(b) With the switch, K, open, adjust the position of the jockey along the bare wire such that l = 0.2 m.
(c) Close the switch K.
(d) Note the ammeter reading, I and voltmeter reading V.
(e) Open the switch K.
(f) Repeat procedures (b) to (e) for values of l = 0.30, 0.40, 0.50, 0.60 and 0.70m.
𝑉
(g) Enter your results in a suitable table including values of 𝐼 .
𝑉
(h) Plot a graph of 𝐼 against l
(i) Find the slope, S, of the graph.
(j) Calculate the resistivity, , of the material of the bare wire from the expression,
 = 2.04 X 10-7 S.
Apparatus: Voltmeter (0-3 V); Ammeter (0 – 1 A); 1 Dry cell; Jockey; Cello tape; 5 pieces of connecting
wires; Metre rule; Switch; Nichrome (28SWG)
57
3.04 Experiment 33
In this experiment, you will determine the internal resistance of a dry cell provided.
(a) Stretch and fix wire P on a metre rule with a cellotape.
(b) Connect the dry cell, 2 Ω resistor and a voltmeter as shown in figure 34 below.
Dry cell
Voltmeter
V
2Ω
Jockey
Cellotape
Cellotape
y
Fig.33
Bare wire, P
(c) Place the jockey on wire P such that y is equal to 30 cm. Record the voltmeter reading v. (d) Repeat
procedure (c) above for values of y equal to 40, 50, 60, 70 and 80 cm
(e) Record your results in a suitable table including values of
𝑦
𝑉
.
𝑦
(f) Plot a graph of 𝑉
(on vertical axis) against y ( on horizontal axis)
(g) Find the slope, s, of the graph.
(h) Find the value n of
(i)
𝑦
𝑉
when y = 0 cm.
Calculate the e.m.f, E of the dry cell from; E =
𝟑𝒙𝟏𝟎−𝟐
𝑺
(j) Calculate the internal resistance, r of the dry cell from; r = 2nE – 1.
Apparatus: Voltmeter (0-3 V); Resistor 2 Ω; Dry cell; Jockey; Cello tape; 5 pieces of connecting wires; Metre
rule; Nichrome (28 SWG).
58
3.05 Experiment 34
In this experiment, you will determine the internal resistance, r of a pair of dry cells.
Fig.34
Procedure
(a) Connect your apparatus as shown in the figure 35 above.
(b) Adjust the distance l= 20 𝑐𝑚
(c) Read and record the voltmeter reading, Vo.
(d) Close Switch K
(e) Read and record the reading of the voltmeter, V1
(f) Open switch K
(g) Repeat procedures (d) to (e) with values of l= 𝟑𝟎, 𝟒𝟎, 𝟓𝟎, 𝟔𝟎 and 𝟕𝟎 𝒄𝒎.
(h) Record your values in a suitable table, including values of
(i) Plot a graph of V against
(j) Find the slope, S of your graph
(k) Calculate the resistance per metre, r, from the expression;
𝒓 = 420𝑺
Apparatus: 2 cells, 2 single cell holders, switch, K, bare wire 110 m long (Constantine wire SWG
28),Voltmeter (0 – 3) V, Cello – tape, metre rule, 2 crocodile clips, 6 Pieces of connecting wires of about
30 cm each.
59
3.06 Experiment 35:
In this experiment, you will determine the diameter,
Procedure
of the bare wire given.
Fig.35
a) Fix the bare wire on the metre rule using the cello – tape.
b) Connect the circuit as shown in the figure 36 above.
c) Adjust the position of the length, 𝒙 = 𝟎. 𝟗𝟎 𝒎.
d) Close the switch, K.
e) Read and record the ammeter reading, and voltmeter reading, .
f) Open the switch, K.
g) Repeat the procedures c) to f) for values of 𝒙 = 𝟎. 𝟖𝟎, 𝟎. 𝟕𝟎, 𝟎. 𝟔𝟎, 𝟎. 𝟓 𝒂𝒏𝒅 𝟎. 𝟒𝟎 𝒄𝒎.
h) Record your results in a suitable table including values of 𝑰𝒙.
i) Plot a graph of
against 𝑰𝒙.
j) Find the slope,
of the graph.
k) Calculate the diameter, D in metres of the bare wire from the expression.
Apparatus: 2 cells, 2 single cell holders, switch, K, bare wire 110 m long (SWG28) , Ammeter (0 – 1) A,
Voltmeter(0 – 3) V, Cello – tape, metre rule, 2 crocodile clips, 5 Pieces of connecting wires of about 30 cm
each.
60
3.07 Experiment 36
In this experiment, you will determine the internal resistance, 𝒓 and the electromotive force,
of the cell.
Fig.36
Procedure:
a) Fix the resistance wire on the metre rule using the cello – tape.
b) Connect the circuit as shown in the fig. 37 above such that AB = 15 cm.
c) Adjust the rheostat until the ammeter reading, = 𝟎. 𝟖𝟎 𝑨.
d) Connect the voltmeter across the cells and record its reading, 𝑽𝟏.
e) Disconnect the voltmeter and connect it across AB. Read and record its reading, 𝑽𝟐
f) Repeat procedures c) to e) for values of 𝑰 = 𝟎. 𝟕𝟎, 𝟎. 𝟔𝟎, 𝟎. 𝟓𝟎, 𝟎. 𝟒𝟎 𝒂𝒏𝒅 𝟎. 𝟑𝟎 𝑨.
g) g) Enter your result in a suitable table.
(h) On the same axes,
i.
Plot a graph of 𝑽𝟏 against. 𝑰
ii. Plot a graph of 𝑽𝟐 against. 𝑰
(i) Read and record the value of current, 𝑰𝟎 and voltmeter, 𝑽𝟎where the two graphs intercept.
(j) Calculate the value of resistance, r from the expression;
Apparatus: 2 cells, 2 single cell holders, switch, K, bare wire 110 m long (SWG28) , Ammeter (0 – 1) A,
Voltmeter (0 – 3) V, Rheostat (0 - 50Ω), Cello – tape, metre rule, 2 crocodile clips, 5 Pieces of connecting
wires of about 30 cm each.
61
3.08 Experiment 37:
In this experiment, you will determine a constant,
of the resistor,
Fig.37
Procedure
a) Connect the circuit as shown in the fig.37 above.
b) Beginning with length, 𝐲 = 𝟎. 𝟐𝟎𝟎 𝐦, close the switch, .
c) Read and record the voltmeter reading,
and the ammeter reading, .
d) Open the switch, .
e) Repeat the procedures (b) to (d) for the values of𝐲 = 𝟎. 𝟑𝟎𝟎, 𝟎. 𝟒𝟎𝟎, 𝟎. 𝟓𝟎𝟎, 𝟎. 𝟔𝟎𝟎 𝐚𝐧𝐝 𝟎. 𝟕𝟎𝟎 𝐦.
f) Record your values in a suitable table including the values of
g) Plot a graph of
.
against
h) Determine the slope,
of the graph.
Apparatus: 2 cells, 2 single cell holders, switch, K, bare wire 110 m long SWG28 , Ammeter (0 – 1) A,
Voltmeter (0 – 3) V, Resistor R, Cello – tape, metre rule, 2 crocodile clips, 5 Pieces of connecting wires of
about 30 cm each.
62
3.09 Experiment 38
In this experiment, you will determine resistance of the filament of the torch bulb provided.
Fig.38
Procedure
a) Connect the circuit as shown on the diagram above.
b) Starting with𝒚 = 𝟏𝟎𝟎 cm and 𝒚𝟎 = 𝟐𝟎 cm, close the switch, K.
c) Read and record the voltmeter reading ,and the ammeter reading, .
d) Open the switch, K.
e) Repeat the procedures (b) to (d) for values of;𝒚𝟎 = 𝟎. 𝟑𝟎𝟎, 𝟎. 𝟒𝟎𝟎, 𝟎. 𝟓𝟎𝟎, 𝟎. 𝟔𝟎𝟎 and 𝟎. 𝟕𝟎𝟎 m.
f)
f) Enter your results in a suitable table.
g) Plot a graph of
against I.
h) Determine the slope, S of the graph.
63
3.10: Experiment 39
In this experiment, you will determine the ratio, p, of the internal resistance of a pair of dry cells to the
resistance per centimetre of the wire labelled, W.
(a) Fix the bare wire labelled, W, on the bench using cello tape.
(b) Connect the circuit as shown in the figure 40 below.
Dry cells
K
Bare
wire
V
l
Fig. 39
Cellotape
Crocodile clips
Cellotape
(c) Starting with a length, l = 20 cm, read and record the voltmeter reading, V0.
(d) Close the switch, K.
(e) Read and record the voltmeter reading, V1.
(f) Open the switch, K.
(g) Repeat the procedures (c) to (f) for values of l= 30, 40, 50, 60 and 70 cm.
(h) Record your values in a suitable table including values of V = V0 – V1 and Plot a graph of V against l.
(i) Determine the slope, p of the graph.
Apparatus: Voltmeter (0-3 V); 2 Dry cells; Jockey; Cello tape; 5 pieces of connecting wires; Metre rule;
Switch, Constantan wire(28 SWG) labelled W.
64
4.11 Experiment 40
In this experiment, you will determine the constant, Lo, of the bicycle spoke
Bicycle spoke
K
Bare wire
A
x
Fig. 40
Crocodile clips
Cellotape
Cellotape
(a) Connect the circuit as shown in figure 41.
(b) Starting with a length, x = 0.800 m, close the switch, K.
(c) Record the ammeter reading, I.
(d) Open the switch K.
(e) Repeat procedures (b) to (d) for values of x = 0.700, 0.600, 0.500, 0.400 and 0.300m.
(f) Record your results in a suitable table including values of
1
𝐼
.
1
(g) Plot a graph of 𝐼
against x.
(h) Find the slope, S, of the graph.
(i) Read the intercept, C, on the
1
𝐼
axis.
(j) Calculate the value of Lo from the expression:
Apparatus: Ammeter (0 – 1 A); 1 Dry cell; Jockey; Cello tape; 5 pieces of connecting wires; Metre rule;
Switch; nichrome (28SWG); Bicycle spoke.
65
4.12 Experiment 41
In this experiment, you will determine the resistance of a resistor.
(a)
Connect the dry cells, resistance wire, resistor R, voltmeter V and ammeter A as shown in
the figure 42 below.
K
100 cm
y
A
Resistance wire
V
Fig. 41
R
(b)
Adjust the length, y, of the resistance wire to 20 cm.
(c)
Close switch K and record the reading V of the voltmeter and I of the ammeter.
(d)
Open switch K.
(e)
Repeat procedures (b) to (c) for values of y equal to 30, 40, 50, 60 and 70 cm.
(f)
Record your results in a suitable table.
(g)
Plot a graph of V against I.
(h)
Find the slope, S of the graph.
Apparatus: Voltmeter (0-3 V); Ammeter (0 – 1A); Resistor 5 ; 2 Dry cells; Jockey; Cello tape; 5 pieces of
connecting wires; Metre rule; Switch; Nichrome (28SWG).
66
4.13 Experiment 42
In this experiment, you will determine the resistance of a resistance wire.
(a) Fix the resistance wire provided firmly on the bench.
(b) Connect the circuit as shown in figure 43 below with the length PQ = 20 cm.
V1
Resistance wire
A
P
Q
Fig. 42
V2
(c) Adjust the rheostat so that the ammeter reading I = 0.6 A.
(d) Connect a voltmeter across the cells and record its reading V1.
(e) Disconnect the voltmeter and connect it across PQ. Record its reading V2.
(f) Repeat procedures (c), (d) and (e) for values of I = 0.5, 0.4, 0.3, 0.2 and 0.1 A.
(g) Record your results in a suitable table.
(h) On the same axes, plot a graph of (i) V1 against I. (ii) V2 against I.
(i) Read the values of current Io and voltage Vo where the two graphs meet.
(j) Calculate the value of
.
Apparatus: Voltmeter (0-3 V); ammeter (0 – 1 A); Rheostat (0 - 50Ω); 2 Dry cells; Jockey; Cello tape; 8
pieces of connecting wires; Metre rule; Switch; Nichrome (28SWG).
67
4.15 Experiment 43.
In this experiment, you will determine the resistance, R, of the filament of the torch bulb provided.
(a)
Fix the bare wire, P, on the bench using pieces of cellotape.
Cellotape
Dry cells
K
xo
x
Bulb
A
Bare wire, P
Crocodile clip
Fig. 43
V
(b)
Connect the circuit as shown in the figure 45 above.
(c)
Starting with length, xo = 1.00 and x = 0.20 m, close the switch, K.
(d)
Read and record the voltmeter reading, V, and the ammeter reading, I.
(e)
Open switch, K.
(f)
Repeat procedures (c) to (e) for values of x = 0.30, 0.40, 0.50, 0.60 and 0.70 m.
(g)
Record your results in a suitable table.
(h)
Plot a graph of V against I.
(i)
Determine the slope, S, of the graph.
Apparatus: 1Voltmeter (0-3 V);1 Ammeter (0 -1); 2 Dry cells; Jockey; 2 pieces of Cello tape; 10 pieces of
connecting wire about 30cm long;1 Metre rule; Constantan (28 SWG); 1 bulb in a holder,1 switch.
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4.16 Experiment 44.
In this experiment, you will determine the constant, β of the bare wire labeled W.
(a)
Connect the circuit shown in figure below
K
Cellotape
A
x
Rheostat
Bare wire, W
Crocodile clip
V
(b)
Adjust the crocodile clip so that x = 0.300m.
(c)
Close switch K, and adjust the rheostat until the ammeter reading, I= 0.40 A.
(d)
Record the voltmeter reading, V.
(e)
Open switch, K.
(f)
Repeat procedures (b) to (e) for values of x = 0.400, 0.500, 0.600, 0.700 & 0.800 m.
(g)
Tabulate your results including values of
(h)
Plot a graph of
(i)
Determine the slope, S, of your graph.
(j)
Calculate the constant, β of the bare wire W from the expression,
against x
β = 1.13x10-7S
Apparatus: 1Voltmeter (0-3 V);1 Ammeter (0 -1); 2 Dry cells; Jockey; 2 pieces of Cello tape; 10 pieces of
connecting wire about 30cm long;1 Metre rule; 1 Switch; Constantan bare wire (28 SWG); 1Rheostat(0 - 50Ω).
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3.17: Experiment 45.
In this experiment, you will determine the constant, R of the resistor provided.
Procedure
a) Set up the apparatus as shown in the diagram above.
b) Starting with length, 𝐋 = 𝟏𝟎𝟎 𝐜𝐦, close the switch, K.
c) Record the voltmeter reading,
and the ammeter readings, .
d) Repeat the procedures b) and c) for values of 𝐋 = 𝟗𝟎, 𝟖𝟎, 𝟕𝟎, 𝟔𝟎and𝟓𝟎 𝐜𝐦.
e) Enter your result in the suitable table including values of
f) Plot a graph of
against
and
.
g) Determine the gradient, S of the graph.
Apparatus: Two cells, Nichrome wire SWG28 (about 110 cm), 8 pieces of connecting wires, a Carbon
resistor, i.e. 5 Ω, ammeter (0 – 1) A, Voltmeter (0 – 3)V, Switch, K, 2 single cell holders.
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